%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU674^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:41 AM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 256 ( 45 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 668 ( 6 ~; 0 |; 21 &; 541 @)
% ( 0 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 29 usr; 6 con; 0-4 aty)
% ( 44 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 194 ( 170 ^; 22 !; 2 ?; 194 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
kpair: $i > $i > $i ).
thf(func_def_7,type,
cartprod: $i > $i > $i ).
thf(func_def_8,type,
singleton: $i > $o ).
thf(func_def_10,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_11,type,
breln: $i > $i > $i > $o ).
thf(func_def_12,type,
func: $i > $i > $i > $o ).
thf(func_def_13,type,
apProp: $o ).
thf(func_def_14,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_22,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_29,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db6:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) )
= singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(f2,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(f3,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(f4,axiom,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
& ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func) ).
thf(f5,axiom,
( apProp
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
@ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apProp) ).
thf(f6,axiom,
( ap
= ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap) ).
thf(f7,conjecture,
( apProp
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app) ).
thf(f8,negated_conjecture,
~ ( apProp
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
( ap
= ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f10,plain,
( ap
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) )
= singleton ),
inference(rectify,[],[f1]) ).
thf(f12,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( apProp
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
@ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f14,plain,
( apProp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 ) ) )
@ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
& ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f18,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f19,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
~ ( apProp
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f21,plain,
( $true
= ( ~ ( apProp
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f23,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f24,plain,
( ap
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f25,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f26,plain,
( apProp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 ) ) )
@ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f27,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f28,plain,
( $true
= ( ~ ( apProp
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( ap @ Y2 @ Y1 @ Y0 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f31,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f23,f22]) ).
thf(f32,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[],[f25,f31,f27]) ).
thf(f33,plain,
( apProp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) )
& ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y2
@ Y1
@ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 ) ) )
@ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f26,f32]) ).
thf(f34,plain,
( $true
= ( ~ ( apProp
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) )
& ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y2
@ Y1
@ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( ^ [Y4: $i,Y5: $i,Y6: $i,Y7: $i] :
( setunion
@ ( dsetconstr @ Y5
@ ^ [Y8: $i] : ( in @ ( kpair @ Y7 @ Y8 ) @ Y6 ) ) )
@ Y2
@ Y1
@ Y0
@ Y3 )
@ Y1 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f28,f32,f24]) ).
thf(f35,plain,
( $true
= ( ~ ( apProp
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y0 ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ Y2 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 ) ) )
@ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
( apProp
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y0 ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ Y2 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 ) ) )
@ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f37,plain,
( ( apProp
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( setadjoin @ Y4 @ emptyset )
= ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y0 ) ) )
& ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ Y2 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 ) ) )
@ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f35]) ).
thf(f38,plain,
( ( apProp
=> apProp )
= $false ),
inference(forward_demodulation,[],[f37,f36]) ).
thf(f39,plain,
$true = $false,
inference(boolean_simplification,[],[f38]) ).
thf(f40,plain,
$false,
inference(trivial_inequality_removal,[],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU674^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:10:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.32 % (3581218)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.32 % (3581227)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3987985781:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.32 % (3581227)Instruction limit reached!
% 0.23/0.32 % (3581227)------------------------------
% 0.23/0.32 % (3581227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581227)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581227)Termination reason: Instruction limit
% 0.23/0.32 % (3581227)Termination phase: Saturation
% 0.23/0.32 % (3581227)Time elapsed: 0.001 s
% 0.23/0.32 % (3581227)Peak memory usage: 11 MB
% 0.23/0.32 % (3581227)Instructions burned: 4 (million)
% 0.23/0.32 % (3581231)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.32 % (3581231)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.32 % (3581225)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3148248329:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.32 % (3581226)lrs+10_16_si=on:nwc=1.5:random_seed=2768886017:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.32 % (3581228)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4137678644:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.32 % (3581229)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2465892554:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.32 % (3581230)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1675239831:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.32 % (3581231)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1330440511:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.32 % (3581236)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2533225916:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.32 % (3581236)Instruction limit reached!
% 0.23/0.32 % (3581236)------------------------------
% 0.23/0.32 % (3581236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581236)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581236)Termination reason: Instruction limit
% 0.23/0.32 % (3581236)Termination phase: Saturation
% 0.23/0.32 % (3581236)Time elapsed: 0.001 s
% 0.23/0.32 % (3581236)Peak memory usage: 12 MB
% 0.23/0.32 % (3581236)Instructions burned: 3 (million)
% 0.23/0.32 % (3581231)Refutation not found, incomplete strategy
% 0.23/0.32 % (3581231)------------------------------
% 0.23/0.32 % (3581231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581231)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581231)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.32 % (3581231)Time elapsed: 0.009 s
% 0.23/0.32 % (3581231)Peak memory usage: 12 MB
% 0.23/0.32 % (3581231)Instructions burned: 15 (million)
% 0.23/0.32 % (3581226)Instruction limit reached!
% 0.23/0.32 % (3581226)------------------------------
% 0.23/0.32 % (3581226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581226)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581226)Termination reason: Instruction limit
% 0.23/0.32 % (3581226)Termination phase: Saturation
% 0.23/0.32 % (3581226)Time elapsed: 0.010 s
% 0.23/0.32 % (3581226)Peak memory usage: 12 MB
% 0.23/0.32 % (3581226)Instructions burned: 18 (million)
% 0.23/0.32 % (3581228)Refutation not found, incomplete strategy
% 0.23/0.32 % (3581228)------------------------------
% 0.23/0.32 % (3581228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581228)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581228)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.32 % (3581228)Time elapsed: 0.010 s
% 0.23/0.32 % (3581228)Peak memory usage: 12 MB
% 0.23/0.32 % (3581228)Instructions burned: 15 (million)
% 0.23/0.32 % (3581231)------------------------------
% 0.23/0.32 % (3581231)------------------------------
% 0.23/0.32 % (3581229)Refutation not found, incomplete strategy
% 0.23/0.32 % (3581229)------------------------------
% 0.23/0.32 % (3581229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581229)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581229)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.32 % (3581229)Time elapsed: 0.010 s
% 0.23/0.32 % (3581229)Peak memory usage: 12 MB
% 0.23/0.32 % (3581229)Instructions burned: 16 (million)
% 0.23/0.32 % (3581228)------------------------------
% 0.23/0.32 % (3581228)------------------------------
% 0.23/0.32 % (3581229)------------------------------
% 0.23/0.32 % (3581229)------------------------------
% 0.23/0.32 % (3581248)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.32 % (3581248)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4086106809:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/0.32 % (3581247)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=718268668:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.32 % (3581248)Instruction limit reached!
% 0.23/0.32 % (3581248)------------------------------
% 0.23/0.32 % (3581248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581248)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581248)Termination reason: Instruction limit
% 0.23/0.32 % (3581248)Termination phase: Saturation
% 0.23/0.32 % (3581248)Time elapsed: 0.003 s
% 0.23/0.32 % (3581248)Peak memory usage: 12 MB
% 0.23/0.32 % (3581248)Instructions burned: 11 (million)
% 0.23/0.32 % (3581251)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.32 % (3581251)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.32 % (3581247)Instruction limit reached!
% 0.23/0.32 % (3581247)------------------------------
% 0.23/0.32 % (3581247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581247)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581247)Termination reason: Instruction limit
% 0.23/0.32 % (3581247)Termination phase: Saturation
% 0.23/0.32 % (3581247)Time elapsed: 0.003 s
% 0.23/0.32 % (3581247)Peak memory usage: 12 MB
% 0.23/0.32 % (3581247)Instructions burned: 6 (million)
% 0.23/0.32 % (3581250)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2275406690:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.23/0.32 % (3581251)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1578319220:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.23/0.32 % (3581252)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2212657799:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.23/0.32 % (3581252) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3581218-3581252"...
% 0.23/0.32 % (3581257)lrs+10_1_si=on:cs=on:random_seed=3638768413:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.23/0.32 % (3581252)...printing done.
% 0.23/0.32 % (3581257)Instruction limit reached!
% 0.23/0.32 % (3581257)------------------------------
% 0.23/0.32 % (3581257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581257)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581257)Termination reason: Instruction limit
% 0.23/0.32 % (3581257)Termination phase: Saturation
% 0.23/0.32 % (3581257)Time elapsed: 0.003 s
% 0.23/0.32 % (3581257)Peak memory usage: 11 MB
% 0.23/0.32 % (3581257)Instructions burned: 13 (million)
% 0.23/0.32 % (3581250)Instruction limit reached!
% 0.23/0.32 % (3581250)------------------------------
% 0.23/0.32 % (3581250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581250)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581250)Termination reason: Instruction limit
% 0.23/0.32 % (3581250)Termination phase: Saturation
% 0.23/0.32 % (3581250)Time elapsed: 0.007 s
% 0.23/0.32 % (3581250)Peak memory usage: 12 MB
% 0.23/0.32 % (3581250)Instructions burned: 13 (million)
% 0.23/0.32 % (3581252)Refutation found. Thanks to Tanya!
% 0.23/0.32 % SZS status Theorem for theBenchmark
% 0.23/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.32 % (3581252)------------------------------
% 0.23/0.32 % (3581252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (3581252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (3581252)CaDiCaL version: 2.1.3
% 0.23/0.32 % (3581252)Termination reason: Refutation
% 0.23/0.32 % (3581252)Time elapsed: 0.005 s
% 0.23/0.32 % (3581252)Peak memory usage: 12 MB
% 0.23/0.32 % (3581252)Instructions burned: 9 (million)
% 0.23/0.32 % (3581218)Success in time 0.06 s
% 0.23/0.32 % Vampire exiting
%------------------------------------------------------------------------------